The Dual of Number Sequences, Riordan Polynomials, and Sheffer Polynomials

Tian-Xiao He, José l Ramírez

Research output: Journal ArticleArticlepeer-review


In this paper we introduce different families of numerical and polynomial sequences by using Riordan pseudo involutions and Sheffer polynomial sequences. Many examples are given including dual of Hermite numbers and polynomials, dual of Bell numbers and polynomials, among other. The coefficients of some of these polynomials are related to the counting of different families of set partitions and permutations. We also studied the dual of Catalan numbers and dual of Fuss-Catalan numbers, giving several combinatorial identities.
Original languageAmerican English
JournalSpecial Matrices
StatePublished - Dec 9 2021


  • Riordan array
  • Dual number sequence
  • Bernoulli numbers and polynomials
  • Fuss-Catalan num-bers
  • Sheer sequence
  • Dual Sheer sequence


  • Physical Sciences and Mathematics
  • Applied Mathematics
  • Mathematics

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